Logic of approximate entailment in quasimetric and in metric spaces

Logic of approximate entailment in quasimetric and in metric spaces It is known that a quasimetric space can be represented by means of a metric space; the points of the former space become closed subsets of the latter one, and the role of the quasimetric is assumed by the Hausdorff quasidistance. In this paper, we show that, in a slightly more special context, a sharpened version of this representation theorem holds. Namely, we assume a quasimetric to fulfil separability in the original sense due to Wilson. Then any quasimetric space can be represented by means of a metric space such that distinct points are assigned disjoint closed subsets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Soft Computing Springer Journals

Logic of approximate entailment in quasimetric and in metric spaces

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by The Author(s)
Subject
Engineering; Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics
ISSN
1432-7643
eISSN
1433-7479
D.O.I.
10.1007/s00500-016-2215-x
Publisher site
See Article on Publisher Site

Abstract

It is known that a quasimetric space can be represented by means of a metric space; the points of the former space become closed subsets of the latter one, and the role of the quasimetric is assumed by the Hausdorff quasidistance. In this paper, we show that, in a slightly more special context, a sharpened version of this representation theorem holds. Namely, we assume a quasimetric to fulfil separability in the original sense due to Wilson. Then any quasimetric space can be represented by means of a metric space such that distinct points are assigned disjoint closed subsets.

Journal

Soft ComputingSpringer Journals

Published: Jun 17, 2016

References

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